Magnetic field asymmetry of transport dynamics in a Coulomb-coupled quantum point contact

We report phase-resolved microwave magnetotransport measurements of a Coulomb-coupled quantum point contact in the edge state regime. We show that the inductive admittance is manifestly asymmetric under reversal of magnetic field, whereas the field-symmetric conductance is observed. Furthermore, the asymmetry is found to exhibit pronounced fluctuations as a function of magnetic field and transmission. This constitutes direct evidence that kinetic effects associated with the nonequilibrium polarization charge contribute to dynamical magnetoasymmetry in phase-coherent mesoscopic conductors. In addition, we find a striking magnetoasymmetry in the electronic transit time, providing important information about Coulomb coupling effects on quantum dynamics of electrons.

Figure 1

(a) Schematic illustrating the device layout. An oscillating voltage $V_{\mathrm{ac}}\left(t\right)=\delta V_1{e}^{-i\omega t}$ is applied at contact 1, which induces the nonequilibrium charge distributions in the constriction defined by two polarized regions ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$. (b) The low-frequency equivalent circuit of the Coulomb-coupled QPC conductor. The dynamical response of this mesoscopic circuit strongly depends on the Coulomb couplings, i.e., $C_0$ and $C_{\mathrm{g}}$, which are specified in the text. (c) Schematic electrical-circuit of the admittance measurement setups based on the false-colour scanning electron micrograph of a typical sample.

Figure 2

(a) Real part ($G_0$) and imagine part ($-\omega E_{21}$) of the admittance as a function of gate voltage for different magnetic fields from $-0.4$ (left) to 0.4 T (right) with an increment of 0.05 T at $f=2.2$ GHz. The curves are shifted by 0.04 V between adjacent traces. The green line (not shifted) corresponds to the data acquired at zero magnetic field. The negative imaginary part denotes an inductive response of the circuit. (b) Color scale of $d{E}_{21}/d{V}_{\mathrm{g}}$ as a function of $B$ and $V_{\mathrm{g}}$. The plateaus appear in light blue, while reddish yellow corresponds to transition between the plateaus. The wine dotted arrows mark position of the ”anomaly” structures of the quantized plateaus. (c) and (d) Nyquist representation ($E_{21}$ vs $G_0$) of the admittance (left axis) at $B=0.11$ and 0.4 T, respectively. Green solid lines show the fit curves with quadratic function, $E={\alpha }_1{G}_0+{\alpha }_2{G}_0^2$. Blue dots indicate relaxation time $\tau$ (right axis) as a function of $V_{\mathrm{g}}$. Insert in (c): magnified view of the time curve at $V_{\mathrm{g}}\le -0.35$ V.

Figure 3

(a) Real and (b) imaginary parts of the magnetoadmittance for various gate voltages as indicated. The voltages are selected from the quantized plateau regions indicated by colored arrows in Fig. 2.

Figure 4

(a) The asymmetric emittance $E_{\mathrm{as}}$ as a function of gate voltage for different magnetic fields. (b) Magnetic field dependence of the Luttinger interaction parameter $g^2$ extracted from the quadratic fits of the emittance in Fig. 2. (c) Magnetic field dependence of the lengthened ergodic time ${\tau }_{\mathrm{er}}$ through the QPC. Red dashed-dotted lines are linear fits to the data, ${\tau }_{\mathrm{er}}\propto B$.